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Category: Algebra

Question-141651

Question Number 141651 by mathsuji last updated on 21/May/21 Commented by MJS_new last updated on 22/May/21 $$\mathrm{it}'\mathrm{s}\:\mathrm{wrong}. \\ $$$${a}={b}={c}=\mathrm{0}\:\Rightarrow\:\mathrm{6}\sqrt{\mathrm{2}}>\mathrm{0} \\ $$$${a}={b}={c}=−\sqrt{\mathrm{3}}\:\Rightarrow\:\mathrm{6}\sqrt{\mathrm{2}}>−\mathrm{6}\sqrt{\mathrm{3}}>−\mathrm{9}\sqrt{\mathrm{3}} \\ $$ Commented by…

Solve-for-real-numbers-5-1-z-1-5-1-z-1-5-2-4-1-z-1-4-1-z-1-4-

Question Number 141654 by mathsuji last updated on 21/May/21 $${Solve}\:{for}\:{real}\:{numbers} \\ $$$$\mathrm{5}\centerdot\left(\sqrt[{\mathrm{5}}]{\mathrm{1}−{z}}\:+\:\sqrt[{\mathrm{5}}]{\mathrm{1}+{z}}\:=\:\mathrm{2}+\mathrm{4}\centerdot\left(\sqrt[{\mathrm{4}}]{\mathrm{1}−{z}}\:+\:\sqrt[{\mathrm{4}}]{\mathrm{1}+{z}}\right)\right. \\ $$ Commented by MJS_new last updated on 22/May/21 $$\mathrm{only}\:\mathrm{solution}\:\mathrm{is}\:{z}=\mathrm{0} \\ $$ Commented…

factorise-x-3-1-

Question Number 10572 by j.masanja06@gmail.com last updated on 18/Feb/17 $$\mathrm{factorise} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1} \\ $$ Answered by sandy_suhendra last updated on 18/Feb/17 $$=\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right) \\…

can-someone-explain-to-me-big-K-notation-I-don-t-know-the-name-It-is-related-to-continuous-fractions-e-g-x-b-0-K-i-1-a-i-b-i-e-x-x-0-0-x-1-1-x-2-2-e-x-i-0

Question Number 10563 by FilupS last updated on 18/Feb/17 $$\mathrm{can}\:\mathrm{someone}\:\mathrm{explain}\:\mathrm{to}\:\mathrm{me} \\ $$$$\mathrm{big}\:\mathrm{K}\:\mathrm{notation}?\:\left(\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{the}\:\mathrm{name}\right) \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{related}\:\mathrm{to}\:\mathrm{continuous}\:\mathrm{fractions}. \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\:{x}={b}_{\mathrm{0}} +\underset{{i}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\mathrm{K}}}}\frac{{a}_{{i}} }{{b}_{{i}} } \\ $$$$\: \\ $$$${e}^{{x}}…

Prove-that-tan-sec-1-tan-tan-1-cot-

Question Number 10542 by FilupS last updated on 17/Feb/17 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{tan}\left(\mathrm{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{tan}\left(\theta\right)}\right)\right)=\sqrt{\mathrm{tan}\left(\theta\right)}\sqrt{\mathrm{1}−\mathrm{cot}\left(\theta\right)} \\ $$ Answered by mrW1 last updated on 17/Feb/17 $${let}\:\alpha=\mathrm{sec}^{−\mathrm{1}} \left(\sqrt{\mathrm{tan}\:\left(\theta\right)}\right) \\…